Edge Version of Doubly Resolving Sets for Grid and Generalized Prism Networks

Abstract

Monitoring and controlling complex networks is of great importance to understand different types of technological and physical systems for source localization. Source localization refers to the process of determining the location or position of a signal source in space based on measurements obtained from multiple sensors. Doubly resolving sets, also known as doubly-resolving arrays, are a particular type of sensor configuration that can enhance the accuracy of source localization. In other words, source localization in a network is equivalent to calculating minimal doubly resolving sets (mDRS) in a network. The concept of the minimal edge version of doubly resolving sets (evDRS) is extension of mDRS. In this article, we take into account the optimization problem of locating the evDRSs for the classes of generalized prism and grid networks. Also, it is demonstrated that the evDRSs for the classes of generalized prisms and grid networks have constant cardinality. This research presents a novel approach with implications for complex network structures such as, network security and communication systems. Furthermore, the findings may have broader implications for diverse fields such as sensor networks, telecommunications, and distributed computing, where prism and grid-like structures are prevalent. The suggested approach may help to improve network optimization and facilitate more robust and reliable grid-based systems.INDEX TERMS Grid networks, Generalized prism networks, Line networks, Doubly resolving sets, Edge computing.